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Almost simultaneously Ritter and Weiss arXiv:1004.2578 on the one hand andKakde arXiv:1008.0142 on the other hand gave a proof of the non-commutativeIwasawa main conjecture over totally real fields for the Tate motive under theassumption that a certain $\mu$-invariant vanishes as has been conjectured alsoby Iwasawa. In this notes we compare both approaches in a survey.

On the work of Ritter and Weiss in Comparison with Kakde's Approach